GCF of 697/34, 104/1354
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 697/34, 104/1354 i.e 1/23018 easily. The following is the detailed procedure to determine the greatest common factor of fractions 697/34, 104/1354.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 697/34,104/1354?
Given fractions are 697/34,104/1354
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 697/34,104/1354, numerators are 697,104
Denominators are 34,1354
The GCF of 697,104 is 1 .
LCM of 34,1354 is 23018.
The greatest common factor of 697/34,104/1354 = [GCF of 697,104]/[LCM of 34,1354]= 1/23018
Therefore, the GCF of 697/34,104/1354 is 1/23018.
To find the highest common factor of 697,104, we have to find the factors of both numbers and list the highest common factor.
The factors of 697 are 1, 17, 41, 697
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The HCF of 697,104 is 1.
Lets's calculate GCF of 697,104
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 697,104 By Matching Biggest Common Factor Method
Now, list down the factors of 697
:1,17,41,697
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Greatest Common Factor
We found the factors 697,104 . The biggest common factor number is the GCF number.
So the greatest common factor 697,104 is 1.
Lets's calculate LCM of 34,1354
| 2 | 34, 1354 |
| 17, 677 |
∴ So the LCM of the given numbers is 2 x 17 x 677 = 23018
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23018
Therefore, the GCF of Fractions 697/34,104/1354 is 1/23018
Least Common Multiple of 34,1354 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 34,1354 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,1354) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,1354) x common factors =2 x 1 = 2
LCM(34,1354) = ( 34 × 1354 ) / 2
LCM(34,1354) = 46036 / 2
LCM(34,1354) = 23018
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FAQs on GCF of Fractions of 697/34, 104/1354
1. What is the HCF of 697,104?
The HCF of 697,104 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 697/34, 104/1354?
Answer: GCF of Numerators as per given numbers 697/34, 104/1354 is
GCF of Numerators i.e. for 697,104 is 1
LCM of denominators i.e. for 34,1354 is 23018.
Thus, GCF of Fractions is 1/23018.Finally, GCF of Fractions for 697/34, 104/1354 is 1/23018.